{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Waves\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/grids/Waves.ipynb)\n",
    "\n",
    "This example simulates waves induced by a moving sphere on a 2D grid.\n",
    "It is a direct port of [this example](https://github.com/NVIDIA/warp/blob/main/warp/examples/core/example_wave.py) from warp."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install --quiet phiflow\n",
    "from phi.jax.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well.\n",
    "from tqdm.notebook import trange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define two functions, `wave_displace` to model the interactions between the obstacle and the height field, and `step` to advance the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def wave_displace(sphere: Sphere, *fields: Field, mag=.5, t=-math.PI * 0.5):\n",
    "    return [field.where(sphere, mag * math.sin(t), f) for f in fields]\n",
    "\n",
    "@jit_compile\n",
    "def step(h_c, h_p, time, dt=1/60./16, k_speed=1.0, k_damp=0.0):\n",
    "    sphere = Sphere(center=h_c.bounds.center + math.rotate_vector(vec(x=0, y=-12.8/3), time), radius=1.)\n",
    "    h_c, h_p = wave_displace(sphere, h_c, h_p)\n",
    "    h_n = 2.0 * h_c - h_p + dt * dt * (k_speed * h_c.laplace() - k_damp * (h_c - h_p))  # wave_solve\n",
    "    return h_n, h_c, time + dt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run the simulation on a $128\\times128$ grid, performing 16 sub-steps per frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6b01b15629ab44ba81b3a50dcb81c1db",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/300 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h_initial = CenteredGrid(x=128, y=128, bounds=Box(x=12.8, y=12.8), boundary=ZERO_GRADIENT)\n",
    "h_trj, *_ = iterate(step, batch(time=300), h_initial, h_initial, 0, substeps=16, range=trange)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
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       "</video>"
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       "<matplotlib.animation.FuncAnimation at 0x23a9c17a5e0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(h_trj.time[::3], animate='time', size=(5, 4))"
   ]
  }
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